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Showing content from https://github.com/scikit-hep/vector below:

scikit-hep/vector: Vector classes and utilities

Vector: arrays of 2D, 3D, and Lorentz vectors

You can install Vector with pip and conda.

Vector is a Python library for 2D and 3D spatial vectors, as well as 4D space-time vectors. It is especially intended for performing geometric calculations on arrays of vectors, rather than one vector at a time in a Python for loop.

Vector is part of the Scikit-HEP project, High Energy Physics (HEP) tools in Python.

Vectors may be expressed in any of these coordinate systems:

the azimuthal plane may be Cartesian x y or polar rho ( $\rho$ ) phi ( $\phi$ )
the longitudinal axis may be Cartesian z, polar theta ( $\theta$ ), or pseudorapidity eta ( $\eta$ )
the temporal component for space-time vectors may be Cartesian t or proper time tau ( $\tau$ )

in any combination. (That is, 4D vectors have 2×3×2 = 12 distinct coordinate systems.)

Vectors may be included in any of these data types:

vector.obj objects (pure Python)
NumPy structured arrays of vectors
Awkward Arrays of vectors (possibly within variable-length lists or nested record structures)
SymPy expressions for symbolic (non-numeric) manipulations
In Numba-compiled functions, with vector.obj objects or Awkward Arrays

Each of these "backends" provides the same suite of properties and methods, through a common "compute" library.

Geometric versus momentum

Finally, vectors come in two flavors:

geometric: only one name for each property or method
momentum: same property or method can be accessed with several synonyms, such as pt ( $p_T$ , transverse momentum) for the azimuthal magnitude rho ( $\rho$ ) and energy and mass for the Cartesian time t and proper time tau ( $\tau$ ).

Names and coordinate conventions were chosen to align with ROOT's TLorentzVector and Math::LorentzVector, as well as scikit-hep/math, uproot-methods TLorentzVector, henryiii/hepvector, and coffea.nanoevents.methods.vector.

Source code on GitHub: scikit-hep/vector
Report bugs and request features on the GitHub Issues page
Ask questions on the GitHub Discussions page
Real-time chat on Gitter: Scikit-HEP/Vector

If you want to contribute to Vector, pull requests are welcome!

Please install the latest version of the main branch from source or a fork:

git clone https://github.com/scikit-hep/vector.git
cd vector
pip install -e .

Refer to CONTRIBUTING.md for more.

To cite Vector, please use

@article{Chopra2025,
doi = {10.21105/joss.07791},
url = {https://doi.org/10.21105/joss.07791},
year = {2025}, publisher = {The Open Journal},
volume = {10},
number = {109},
pages = {7791},
author = {Saransh Chopra and Henry Schreiner and Eduardo Rodrigues and Jonas Eschle and Jim Pivarski},
title = {Vector: JIT-compilable mathematical manipulations of ragged Lorentz vectors},
journal = {Journal of Open Source Software}
}

Papers and talks

Thanks goes to these wonderful people (emoji key):

This project follows the all-contributors specification. Contributions of any kind welcome! See CONTRIBUTING.md for information on setting up a development environment.

This library was primarily developed by Saransh Chopra, Henry Schreiner, Jim Pivarski, Eduardo Rodrigues, and Jonas Eschle.

Support for this work was provided by the National Science Foundation cooperative agreement OAC-1836650 and PHY-2323298 (IRIS-HEP) and OAC-1450377 (DIANA/HEP). Any opinions, findings, conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

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